A theory that describes how matter produces and responds to the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

learn more… | top users | synonyms (1)

5
votes
1answer
439 views

Interpretation of the Einstein-Hilbert action

Everyone knows the famous Einstein-Hilbert action $S_{EH} = \int d^4x \sqrt{-g} R$. I'd like to know if, after we first explicit the Ricci scalar in terms of the metric, it could be possible to ...
2
votes
2answers
320 views

How does gravitation propagate along curved spacetime?

In this wikipedia article it is described how a beam of light, with its locally constant speed, can travel "faster than light". That is to say it travels a distance, which, from a special relativistic ...
-1
votes
2answers
467 views

shouldn't gravity travel at light speed immediately

if gravity travels at c(light speed), why aren't objects pulled to earth at that speed? Since the velocity of gravity is 9.8 meters per second squared, will it eventually accelerate until it maxes ...
10
votes
5answers
763 views

How does the string worldsheet affect the space-time in which they live?

I don't understand much about string theory and never really got much further past the Nambu-Goto action and very basic supersymmetry (SUSY) lectures in my undergraduate courses, but the only thing ...
2
votes
2answers
2k views

Are neutrinos affected by gravity?

Layman here, but EE and BS physics. I know that light is affected by gravity. But are neutrinos? During the collapse of a star into a neutron star, as the electrons join protons to form neutrons ...
19
votes
0answers
692 views

A dictionary of string - standard physics correspondences

Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 ...
3
votes
0answers
749 views

Derivation of the Gauss-Codazzi equation

I'm interested in the derivation of the Gauss equation (Gauss-Codazzi). Usually we consider the definition of the Riemann tensor on the hypersurface. $$^{(n-1)}R_{abc}^{~~~~~~~d}~w_d=[D_a,D_b]w_c$$ ...
3
votes
2answers
204 views

Clarification on Wald's book

I have a question concerning the Wald's book: General Relativity. In the appendix E, he derived the Einstein equation by considering the surface term (GHY). I do not understand what he said after the ...
17
votes
4answers
441 views

What does the equivalence principle mean in quantum cases?

We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear. So is there any similar situation in the case of electron near the ...
1
vote
1answer
339 views

What is the fate of a 3-Torus universe?

Since it is flat, will it expand forever like a flat and open universe or collapse like a closed and curved universe?
0
votes
2answers
243 views

How can we model intrinsic curvature?

Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?
1
vote
1answer
377 views

Why is the universe described in terms of Euclidean space and not Minkowski spacetime?

The universe is described as an infinite Euclidean space in cosmology. Why isn't it treated as Minkowski spacetime?
1
vote
2answers
260 views

How to deal with the product of distributions by Renormalization or similar?

how can we deal for example with the product of distributions in physics ?? is there any mean to define with physics $ \delta ^{2}(x) $ or to treat a product of two distributions within the ...
4
votes
3answers
257 views

Twin paradox - observers counter orbiting Earth

Imagine three observers - one (A) stationary on the surface of Earth (latitude 0 deg) and two others orbiting the planet in the same circular equatorial orbit just in the opposite direction. When the ...
4
votes
1answer
176 views

Simulating a black hole binary system

As part of a project for my degree I am writing code to simulate N-body gravitational interactions, however I have to then use this code to investigate something. Struggling to think of ideas I ...
8
votes
5answers
474 views

What makes the stars that are farther from the nucleus of the galaxy go faster than those in the middle?

It has no sense that stars that have a bigger radius and apparently less angular speed($\omega$) goes faster than the ones near the center.
2
votes
2answers
1k views

Faster-than-light communication using Alcubierre warp drive metric around a single qubit?

The Alcubierre warp drive metric has been criticized on the points of requiring a large amount of exotic matter with negative energy, and conditions deadly for human travellers inside the bubble. What ...
1
vote
2answers
965 views

How do we determine the temperature of a Black Hole?

How do we determine the temperature of a Black Hole? Since we cannot see a Black Hole, which I presume, is because it absorbs light, would it not also prevent radiation from escaping, making ...
5
votes
1answer
2k views

Why is light described by a null geodesic?

I'm trying to wrap my head around how geodesics describe trajectories at the moment. I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
1
vote
2answers
297 views

Computing the path of photons near a black hole

For a simulation, I want to compute the path that light follows near a black hole. Non-relativistically, a massive point particle in a central newtonian gravitational field follows either an ellipse, ...
6
votes
1answer
389 views

Do spacelike junctions in the Thin-Shell Formalism imply energy nonconservation and counterintuitive wormholes?

The Thin Shell Formalism (MTW 1973 p.551ff) is used to properly paste together different vacuum solutions to the Einstein equations. At the junction of the two solutions is a hypersurface of matter – ...
-2
votes
2answers
107 views

The relativistic mechanics of a battery that is being charged and accelerated at the same time

This might be an interesting question: Let's attach a battery into one end of an electric cable. Then we rotate the battery around, with accelerating speed, using 100 Watts of power, while the ...
18
votes
2answers
3k views

Does a photon exert a gravitational pull?

I know a photon has zero rest mass, but it does have plenty of energy. Since energy and mass are equivalent does this mean that a photon (or more practically, a light beam) exerts a gravitational pull ...
1
vote
2answers
1k views

Abstract Algebra in Relativity and Cosmology?

Is Abstract Algebra useful in theoretical Relativity and/or Cosmology? If so can anyone give me some examples or point me towards a good book with that emphasis if it is one? Thanks in advance.
9
votes
3answers
611 views

Why does large curvature of spacetime imply high temperature?

I`ve just stumbled about a sentence which says that high curvature of spacetime implies that any matter present is at high temperature. This somehow confuses me, so my probably dumb question(s) are: ...
4
votes
2answers
244 views

Are we going to be able to travel trough space deforming the space-time?

I'm not talking about the speed of the spaceship. If we can deform space-time we needn't any type of propulsion. And how can the travel affect to it's pilots? Can they survive?
11
votes
2answers
609 views

Equivalence of definitions of ADM Mass

ADM Mass is a useful measure of a system. It is often defined (Wald 293) $$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$ Where $s_r$ is two ...
5
votes
3answers
260 views

Tension on a cable in a gravitational field

Consider a mass 'm' suspended in the gravitational field of a massive star. Assuming the Schwarzschild metric it is easy to calculate the gravitational acceleration at the location of the mass and ...
5
votes
3answers
593 views

Does spacetime in general relativity contain holes?

Are there physical models of spacetimes, which have bounded (four dimensional) holes in them? And do the Einstein equations give restrictions to such phenomena? Here by holes I mean ...
2
votes
3answers
331 views

Evidence that “space exists rather than just particles”

What is (theoretical) evidence that you need to define all of space with properties rather than just stating where all particles are? I mean, does every single coordinate x, y, z have a meaning or ...
7
votes
2answers
671 views

Lorentz invariance of the 3 + 1 decomposition of spacetime

Why is allowed decompose the spacetime metric into a spatial part + temporal part like this for example $$ds^2 ~=~ (-N^2 + N_aN^a)dt^2 + 2N_adtdx^a + q_{ab}dx^adx^b$$ ($N$ is called lapse, $N_a$ is ...
2
votes
1answer
212 views

Derivative of quantities with internal indices

In the context of the 3 + 1 decomposition of spacetime needed for a Hamiltionian formulation of general relativity, quantities with so called internal indices are introduced (in the book I am reading ...
2
votes
1answer
141 views

Question from Schutz's

In q. 22 in page 141, I am asked to show that if $U^{\alpha}\nabla_{\alpha} V^{\beta} = W^{\beta}$, then $U^{\alpha}\nabla_{\alpha}V_{\beta}=W_{\beta}$. Here's what I have done: $V_{\beta}=g_{\beta ...
1
vote
2answers
323 views

Finding the correct units for the energy-momentum tensor?

I'm trying to understand the energy-momentum tensor $T^{\mu\nu}$ but I'm confused about the units. My textbook says the components of $T^{\mu\nu}$ are $\mathrm{Jm^{-3}}$. Four-momentum is is given ...
2
votes
1answer
387 views

How do I calculate the induced metric in the Gibbons–Hawking–York boundary term?

This question concerns the expression for the induced metric in the explicit variation of the GHY boundary term. Just how is that expression derived in detail from the definition of the induced metric ...
6
votes
3answers
286 views

From the perspective of an observer inside a black hole's horizon, where does the energy for Hawking radiation come from?

Would energy be seen to "flow" to the outside of the black hole? Through what mechanism?
5
votes
1answer
160 views

Hawking radiation: direct matter -> energy conversion?

When a black hole evaporates, does it turn all the matter that has fallen in directly to energy, or will it somehow throw back out the same kind of matter (normal or anti) that went in?
19
votes
5answers
2k views

Does a charged particle accelerating in a gravitational field radiate?

A charged particle undergoing an acceleration radiates photons. Let's consider a charge in a freely falling frame of reference. In such a frame, the local gravitational field is necessarily zero, ...
5
votes
3answers
198 views

Analyticity and Causality in Relativity

A few weeks ago at a conference a speaker I was listening to made a comment to the effect that a function (let's say scalar) cannot be analytic because otherwise it would violate causality. He didn't ...
6
votes
2answers
715 views

Deriving Birkhoff's Theorem

I am trying to derive Birkhoff's theorem in GR as an exercise: a spherically symmetric gravitational field is static in the vacuum area. I managed to prove that $g_{00}$ is independent of t in the ...
5
votes
2answers
254 views

What should be the equation satisfied by The Momentum commutators in a curved background?

This may be obvious but I have limited experience in physics , The generators of Spatial translation symmetry commutes with each other i.e [P(i),P(j)] = 0 but if Spacetime is a curved manifolds then ...
8
votes
2answers
911 views

Have red shifted photons lost energy and where did it go?

I think the title says it. Did expansion of the universe steal the energy somehow?
7
votes
2answers
449 views

Equivalence principle and radiation from falling particle

I am currently having a hard time solving a problem of GR from Lasenby's book. I can't make it more clear than by quoting the exercise: 7.2 A charged object held stationary in a laboratory on the ...
4
votes
2answers
322 views

Potential energy conservation in traversable wormholes

Let's say I have a tube, of large radius (about 5 - 7 meters in diameter), with traversable wormholes at the ends. The wormholes are arranged as such that if something falls inside one hole from ...
3
votes
5answers
909 views

Can you use a wormhole to travel through space not time?

I want to know if you could theoretically travel from your house to work via a wormhole but stay in the present day...without changing time. Kind of like teleportation but harnessing the energy of a ...
2
votes
1answer
273 views

Experimental proof of gravitational redshift of light

Has the gravitational red shift been proven for electromagnetic waves only or also for a single photon?
33
votes
12answers
4k views

How can anything ever fall into a black hole as seen from an outside observer?

The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a ...
4
votes
1answer
722 views

Stokes' theorem in GR

I read this formula in Sean Carroll's book of GR: $$\int_{\Sigma}\nabla_{\mu}V^{\mu}\sqrt{g}d^nx~=~\int_{\partial\Sigma}n_{\mu}V^{\mu}\sqrt{\gamma}d^{n-1}x$$ where n is the 4-vector orthogonal to ...
2
votes
1answer
645 views

Discrete point particles stress energy tensor

I am trying to solve an exercise in Sean Carroll's GR book "Spacetime and Geometry". Basically we need to derive the stress-energy tensor of a perfect fluid (ie $T^{\mu\nu}=(\rho +p)U^{\mu}U^{\nu} + ...
2
votes
2answers
130 views

How to test whether galaxies are moving away from each other in a static background or whether space is being created beween them?

Observations show that galaxies are moving away from one another on the macroscopic scale. Now, scientists interpret this by saying this happens not because galaxies are really moving away from each ...